We conduct a numerical investigation into wave propagation and localization in one-dimensional lattices subject to nonlinear disorder, focusing on cases with fixed input conditions. Utilizing a discrete nonlinear Schr"odinger equation with Kerr-type nonlinearity and a random coefficient, we compute the averages and variances of the transmittance, $T$, and its logarithm, as functions of the system size $L$, while maintaining constant intensity for the incident wave. In cases of purely nonlinear disorder, we observe power-law localization characterized by $langle T rangle propto L^{-gamma_a}$ and $langle ln T rangle approx -gamma_g ln L$ for sufficiently large $L$. At low input intensities, a transition from exponential to power-law decay in $langle T rangle$ occurs as $L$ increases. The exponents $gamma_a$ and $gamma_g$ are nearly identical, converging to approximately 0.5 as the strength of the nonlinear disorder, $beta$, increases. Additionally, the variance of $T$ decays according to a power law with an exponent close to 1, and the variance of $ln T$ approaches a small constant as $L$ increases. These findings are consistent with an underlying log-normal distribution of $T$ and suggest that wave propagation behavior becomes nearly deterministic as the system size increases. When both linear and nonlinear disorders are present, we observe a transition from power-law to exponential decay in transmittance with increasing $L$ when the strength of linear disorder, $V$, is less than $beta$. As $V$ increases, the region exhibiting power-law localization diminishes and eventually disappears when $V$ exceeds $beta$, leading to standard Anderson localization.
我们对非线性无序一维晶格中的波传播和定位进行了数值研究，重点是具有固定输入条件的情况。利用具有 Kerr 型非线性和随机系数的离散非线性 Schr"odingerequation，我们计算了透射率 $T$ 及其对数作为系统大小 $L$ 的函数的平均值和方差，同时保持入射波的强度不变。在纯粹非线性无序的情况下，我们观察到功率定位的特征是：在足够大的 L 值下，角 T 和角 L 的对数为 L^{-gamma_a}$ 和角 T 和角 L 的对数为近似-gamma_g ln L$ 。在输入强度较低时，随着 $L 的增加，$langle T （rangle）会从指数衰减过渡到幂律衰减。指数$gamma_a$和$gamma_g$几乎相同，随着非线性无序强度$beta$的增加，指数趋近于约0.5。此外，随着 $L$ 的增加，$T$ 的方差按照指数接近 1 的幂律衰减，而 $ln T$ 的方差接近一个小常数。这些发现与 $T$ 的基本对数正态分布一致，并表明随着系统规模的增大，波的传播行为变得近乎确定性。当线性紊乱和非线性紊乱同时存在时，当线性紊乱的强度 $V$ 小于 $beta$ 时，我们观察到透射率在 $L$ 增加时从幂律衰减过渡到指数衰减。
{"title":"Power-law localization in one-dimensional systems with nonlinear disorder under fixed input conditions","authors":"Ba Phi Nguyen, Kihong Kim","doi":"arxiv-2408.09339","DOIUrl":"https://doi.org/arxiv-2408.09339","url":null,"abstract":"We conduct a numerical investigation into wave propagation and localization\u0000in one-dimensional lattices subject to nonlinear disorder, focusing on cases\u0000with fixed input conditions. Utilizing a discrete nonlinear Schr\"odinger\u0000equation with Kerr-type nonlinearity and a random coefficient, we compute the\u0000averages and variances of the transmittance, $T$, and its logarithm, as\u0000functions of the system size $L$, while maintaining constant intensity for the\u0000incident wave. In cases of purely nonlinear disorder, we observe power-law\u0000localization characterized by $langle T rangle propto L^{-gamma_a}$ and\u0000$langle ln T rangle approx -gamma_g ln L$ for sufficiently large $L$. At\u0000low input intensities, a transition from exponential to power-law decay in\u0000$langle T rangle$ occurs as $L$ increases. The exponents $gamma_a$ and\u0000$gamma_g$ are nearly identical, converging to approximately 0.5 as the\u0000strength of the nonlinear disorder, $beta$, increases. Additionally, the\u0000variance of $T$ decays according to a power law with an exponent close to 1,\u0000and the variance of $ln T$ approaches a small constant as $L$ increases. These\u0000findings are consistent with an underlying log-normal distribution of $T$ and\u0000suggest that wave propagation behavior becomes nearly deterministic as the\u0000system size increases. When both linear and nonlinear disorders are present, we\u0000observe a transition from power-law to exponential decay in transmittance with\u0000increasing $L$ when the strength of linear disorder, $V$, is less than $beta$.\u0000As $V$ increases, the region exhibiting power-law localization diminishes and\u0000eventually disappears when $V$ exceeds $beta$, leading to standard Anderson\u0000localization.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The mobility edge (ME) is a fundamental concept in the Anderson localized systems, which marks the energy separating extended and localized states. Although the ME and localization phenomena have been extensively studied in non-Hermitian (NH) quasiperiodic tight-binding models, they remain limited to NH continuum systems. Here, we investigate the ME and localization properties of a one-dimensional (1D) NH quasiperiodic continuous system, which is described by a Schr{"o}dinger equation with an imaginary vector potential and an incommensurable one-site potential. We find that the ME is located in the real spectrum and falls between the localized and extended states. Additionally, we show that under the periodic boundary condition, the energy spectrum always exhibits an open curve representing high-energy extended electronic states characterized by a non-zero integer winding number. This complex spectrum topology is closely connected with the non-Hermitian skin effect (NHSE) observed under open boundary conditions, where the eigenstates of the bulk bands accumulate at the boundaries. Furthermore, we analyze the critical behavior of the localization transition and obtain critical potential amplitude accompanied by the universal critical exponent $nu simeq 1/3$. Our study provides valuable inspiration for exploring MEs and localization behaviors in NH quasiperiodic continuous systems.
迁移率边沿（ME）是安德森局域系统中的一个基本概念，它标志着扩展态与局域态之间的能量分界线。虽然ME和局域化现象在非赫米提（NH）准周期紧约束模型中得到了广泛的研究，但它们仍然局限于NH连续系统。在这里，我们研究了一维（1D）NH 准周期连续系统的 ME 和局域化特性，该系统由一个具有虚矢量势和不可比单位势的 Schr{"o}dinger 方程描述。此外，我们还发现，在周期性边界条件下，能谱总是呈现出一条开放曲线，代表着以非零整数绕组数为特征的高能扩展电子态。这种复杂的能谱拓扑结构与在开放边界条件下观察到的非赫米梯斯金效应（NHSE）密切相关，在这种情况下，体带的特征状态在边界处聚集。此外，我们还分析了局域化转变的临界行为，并得到了临界势幅以及普遍临界指数 $nu simeq 1/3$。我们的研究为探索 NH 准周期连续系统中的 ME 和局域化行为提供了宝贵的启发。
{"title":"Localization and mobility edges in non-Hermitian continuous quasiperiodic systems","authors":"Xiang-Ping Jiang, Zhende Liu, Yayun Hu, Lei Pan","doi":"arxiv-2408.07585","DOIUrl":"https://doi.org/arxiv-2408.07585","url":null,"abstract":"The mobility edge (ME) is a fundamental concept in the Anderson localized\u0000systems, which marks the energy separating extended and localized states.\u0000Although the ME and localization phenomena have been extensively studied in\u0000non-Hermitian (NH) quasiperiodic tight-binding models, they remain limited to\u0000NH continuum systems. Here, we investigate the ME and localization properties\u0000of a one-dimensional (1D) NH quasiperiodic continuous system, which is\u0000described by a Schr{\"o}dinger equation with an imaginary vector potential and\u0000an incommensurable one-site potential. We find that the ME is located in the\u0000real spectrum and falls between the localized and extended states.\u0000Additionally, we show that under the periodic boundary condition, the energy\u0000spectrum always exhibits an open curve representing high-energy extended\u0000electronic states characterized by a non-zero integer winding number. This\u0000complex spectrum topology is closely connected with the non-Hermitian skin\u0000effect (NHSE) observed under open boundary conditions, where the eigenstates of\u0000the bulk bands accumulate at the boundaries. Furthermore, we analyze the\u0000critical behavior of the localization transition and obtain critical potential\u0000amplitude accompanied by the universal critical exponent $nu simeq 1/3$. Our\u0000study provides valuable inspiration for exploring MEs and localization\u0000behaviors in NH quasiperiodic continuous systems.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and graph-based features such as centrality and clustering coefficients. These topological features outperform conventional features based on Euclidean metric in predicting particle mobility and allow to correctly identify phase transitions as well. These results provide a new set of computational tools to investigate the dynamical properties of condensed matter systems.
{"title":"Graph-Based Feature Engineering to Predict the Dynamical Properties of Condensed Matter","authors":"An Wang, Gabriele C. Sosso","doi":"arxiv-2408.06016","DOIUrl":"https://doi.org/arxiv-2408.06016","url":null,"abstract":"We present a graph theory-based method to characterise flow defects and\u0000structural shifts in condensed matter. We explore the connection between\u0000dynamical properties, particularly the recently introduced concept of\u0000''softness'', and graph-based features such as centrality and clustering\u0000coefficients. These topological features outperform conventional features based\u0000on Euclidean metric in predicting particle mobility and allow to correctly\u0000identify phase transitions as well. These results provide a new set of\u0000computational tools to investigate the dynamical properties of condensed matter\u0000systems.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thales F. Macedo, Julián Faúndez, Raimundo R. dos Santos, Natanael C. Costa, Felipe A. Pinheiro
We theoretically investigate the effects of criticality and multifractal states in a one-dimensional Aubry-Andre-Harper model coupled to electromagnetic cavities. We focus on two specific cases where the phonon frequencies are $omega_{0}=1$ and $omega_{0}=2$, respectively. Phase transitions are analyzed using both the average and minimum inverse participation ratio to identify metallic, fractal, and insulating states. We provide numerical evidence to show that the presence of the optical cavity induces a critical, intermediate phase in between the extended and localized phases, hence drastically modifying the traditional transport phase diagram of the Aubry-Andre-Harper model, in which critical states can only exist at the well-defined metal-insulator critical point. We also investigate the probability distribution of the inverse participation ratio and conduct a multifractal analysis to characterize the nature of the critical phase, in which we show that extended, localized, and fractal eigenstates coexist. Altogether our findings reveal the pivotal role that the coupling to electromagnetic cavities plays in tailoring critical transport phenomena at the microscopic level of the eigenstates.
{"title":"Multifractal critical phase driven by coupling quasiperiodic systems to electromagnetic cavities","authors":"Thales F. Macedo, Julián Faúndez, Raimundo R. dos Santos, Natanael C. Costa, Felipe A. Pinheiro","doi":"arxiv-2408.06496","DOIUrl":"https://doi.org/arxiv-2408.06496","url":null,"abstract":"We theoretically investigate the effects of criticality and multifractal\u0000states in a one-dimensional Aubry-Andre-Harper model coupled to electromagnetic\u0000cavities. We focus on two specific cases where the phonon frequencies are\u0000$omega_{0}=1$ and $omega_{0}=2$, respectively. Phase transitions are analyzed\u0000using both the average and minimum inverse participation ratio to identify\u0000metallic, fractal, and insulating states. We provide numerical evidence to show\u0000that the presence of the optical cavity induces a critical, intermediate phase\u0000in between the extended and localized phases, hence drastically modifying the\u0000traditional transport phase diagram of the Aubry-Andre-Harper model, in which\u0000critical states can only exist at the well-defined metal-insulator critical\u0000point. We also investigate the probability distribution of the inverse\u0000participation ratio and conduct a multifractal analysis to characterize the\u0000nature of the critical phase, in which we show that extended, localized, and\u0000fractal eigenstates coexist. Altogether our findings reveal the pivotal role\u0000that the coupling to electromagnetic cavities plays in tailoring critical\u0000transport phenomena at the microscopic level of the eigenstates.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The microscopic understanding of the dramatic increase in viscosity of liquids when cooled towards the glass transition is a major unresolved issue in condensed matter physics. Here, we use machine learning methods to accelerate molecular dynamics simulations with first-principles accuracy for the glass-former toluene. We show that the increase in viscosity is intimately linked to the increasing number of dynamically correlated molecules $N^*$. While certain hallmark features of glassy dynamics, like physical aging, are linked to $N^*$ as well, others, like relaxation stretching, are not.
{"title":"Glassy Dynamics from First-Principles Simulations","authors":"Florian Pabst, Stefano Baroni","doi":"arxiv-2408.05528","DOIUrl":"https://doi.org/arxiv-2408.05528","url":null,"abstract":"The microscopic understanding of the dramatic increase in viscosity of\u0000liquids when cooled towards the glass transition is a major unresolved issue in\u0000condensed matter physics. Here, we use machine learning methods to accelerate\u0000molecular dynamics simulations with first-principles accuracy for the\u0000glass-former toluene. We show that the increase in viscosity is intimately\u0000linked to the increasing number of dynamically correlated molecules $N^*$.\u0000While certain hallmark features of glassy dynamics, like physical aging, are\u0000linked to $N^*$ as well, others, like relaxation stretching, are not.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The rise of domain-specific computing has led to great interest in Ising machines, dedicated hardware accelerators tailored to solve combinatorial optimization and probabilistic sampling problems. A key element of Ising machines is stochasticity, which enables a wide exploration of configurations, thereby helping avoid local minima. Here, we evaluate and improve the previously proposed concept of coupled chaotic bits (c-bits) that operate without any explicit stochasticity. We show that augmenting chaotic bits with stochasticity leads to better algorithmic scaling in combinatorial optimization problems, comparable to the performance of probabilistic bits (p-bits) which have explicit randomness in their update rules. We first demonstrate that c-bits surprisingly follow the quantum Boltzmann law in a 1D transverse field Ising model, despite the lack of explicit randomness. We then show that c-bits exhibit critical dynamics similar to those of stochastic p-bits in 2D Ising and 3D spin glass models, with promising potential to solve challenging optimization problems. Finally, we propose a noise-augmented version of coupled c-bits via the powerful adaptive parallel tempering algorithm (APT). The noise-augmented c-bit algorithm outperforms fully deterministic c-bits running versions of the simulated annealing algorithm. Chaotic Ising machines closely resemble coupled oscillator-based Ising machines, as both schemes exploit nonlinear dynamics for computation. Oscillator-based Ising machines may greatly benefit from our proposed algorithm, which runs replicas at constant temperature, eliminating the need to globally modulate coupling strengths. Mixing stochasticity with deterministic c-bits creates a powerful hybrid computing scheme that can bring benefits in scaled, asynchronous, and massively parallel hardware implementations.
随着特定领域计算的兴起，人们对专门用于解决组合优化和概率采样问题的专用硬件加速器 Isingmachines 产生了浓厚兴趣。随机性是 Isingmachines 的一个关键要素，它可以广泛探索各种配置，从而帮助避免局部最小值。在此，我们对之前提出的耦合混沌比特（c-bits）概念进行了评估和改进。我们的研究表明，在组合优化问题中，用随机性增强混沌比特能带来更好的算法扩展，其性能可与在更新规则中具有显式随机性的概率比特（p-bits）相媲美。我们首先证明，尽管没有明确的随机性，但在一维横向场兴模型中，c 位出人意料地遵循量子波尔兹曼定律。然后，我们证明了 c-bit 在二维伊辛模型和三维自旋玻璃模型中表现出与随机 p-bit 类似的临界动力学，有望解决具有挑战性的优化问题。最后，我们通过功能强大的自适应并行回火算法（APT），提出了耦合 c-bit 的噪声增强版本。噪声增强 c 位算法优于运行模拟退火算法版本的完全确定性 c 位算法。混沌伊辛机与基于振荡器的耦合伊辛机非常相似，因为这两种方案都利用非线性动力学进行计算。我们提出的算法在恒定温度下运行副本，无需全局调节耦合强度，因此基于振荡器的伊兴机可以从我们的算法中受益匪浅。
{"title":"Noise-augmented Chaotic Ising Machines for Combinatorial Optimization and Sampling","authors":"Kyle Lee, Shuvro Chowdhury, Kerem Y. Camsari","doi":"arxiv-2408.04744","DOIUrl":"https://doi.org/arxiv-2408.04744","url":null,"abstract":"The rise of domain-specific computing has led to great interest in Ising\u0000machines, dedicated hardware accelerators tailored to solve combinatorial\u0000optimization and probabilistic sampling problems. A key element of Ising\u0000machines is stochasticity, which enables a wide exploration of configurations,\u0000thereby helping avoid local minima. Here, we evaluate and improve the\u0000previously proposed concept of coupled chaotic bits (c-bits) that operate\u0000without any explicit stochasticity. We show that augmenting chaotic bits with\u0000stochasticity leads to better algorithmic scaling in combinatorial optimization\u0000problems, comparable to the performance of probabilistic bits (p-bits) which\u0000have explicit randomness in their update rules. We first demonstrate that\u0000c-bits surprisingly follow the quantum Boltzmann law in a 1D transverse field\u0000Ising model, despite the lack of explicit randomness. We then show that c-bits\u0000exhibit critical dynamics similar to those of stochastic p-bits in 2D Ising and\u00003D spin glass models, with promising potential to solve challenging\u0000optimization problems. Finally, we propose a noise-augmented version of coupled\u0000c-bits via the powerful adaptive parallel tempering algorithm (APT). The\u0000noise-augmented c-bit algorithm outperforms fully deterministic c-bits running\u0000versions of the simulated annealing algorithm. Chaotic Ising machines closely\u0000resemble coupled oscillator-based Ising machines, as both schemes exploit\u0000nonlinear dynamics for computation. Oscillator-based Ising machines may greatly\u0000benefit from our proposed algorithm, which runs replicas at constant\u0000temperature, eliminating the need to globally modulate coupling strengths.\u0000Mixing stochasticity with deterministic c-bits creates a powerful hybrid\u0000computing scheme that can bring benefits in scaled, asynchronous, and massively\u0000parallel hardware implementations.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Multiple trapping and release (MTR) is a typical transport mechanism of electron carriers in amorphous and other disordered semiconductors where localized states are significant. Quantitative description of MTR, however, has been based on an "abrupt" mobility edge model, which relies on two underpinning simplifications: (i) states above the conduction band mobility edge are extended and any of them is omnipresent in space, whereas states below the mobility edge are localized and they exist in space as pointlike sites; (ii) all states are evenly distributed in space, and the local density of states (DOS) distribution is spatially invariant. The prequel to this paper [Y. Luo and A. J. Flewitt, Phys. Rev. B 109, 104203 (2024)] demonstrates that neither of these simplifications is valid. Hence, this paper reinvestigates MTR transport and focuses on two similar scenarios: steady DC conduction and non-dispersive time-of-flight conduction. We have managed to reveal that, first, the experimentally measured mobility edge is an effective quantity which is different from the actual critical energy that demarcates extended states and localized states of an amorphous semiconductor. Second, the experimentally derived extended-state mobility is also an effective quantity which turns out to be higher than the actual mobility of free electrons in the material. These two effective quantities are quantified using the hydrogenated amorphous silicon (a-Si:H) discussed in the prequel paper as an example.
多重捕获和释放（MTR）是无定形半导体和其他无序半导体中电子载流子的一种典型传输机制，其中局部态非常重要。然而，对 MTR 的定量描述一直基于 "突变 "迁移率边沿模型，该模型依赖于两个基本原理：(i) 导带迁移率边沿以上的态是扩展的，它们中的任何一个在空间中都是无所不在的，而迁移率边沿以下的态是局部的，它们以点状位点的形式存在于空间中；(ii) 所有的态在空间中都是均匀分布的，而且局部的态密度（DOS）分布在空间上是不变的。本文的前传[Y. Luo and A. J. Flewitt, Phys. Rev. B 109, 104203 (2024)]证明了上述简化都不成立。因此，本文重新研究了 MTR 传输，并把重点放在两种类似的情况上：稳定的直流传导和非分散的飞行时间传导。我们成功地揭示出：首先，实验测量到的迁移率边缘是一个有效量，它不同于划分非晶半导体扩展态和局部态的实际临界能量。其次，实验得出的扩展态迁移率也是一个有效量，它高于材料中自由电子的实际迁移率。我们以前篇论文中讨论的氢化非晶硅（a-Si:H）为例，对这两个有效量进行了量化。
{"title":"Revisiting multiple trapping and release electronic transport in amorphous semiconductors exemplified by a-Si:H","authors":"Yuezhou Luo, Andrew John Flewitt","doi":"arxiv-2408.03678","DOIUrl":"https://doi.org/arxiv-2408.03678","url":null,"abstract":"Multiple trapping and release (MTR) is a typical transport mechanism of\u0000electron carriers in amorphous and other disordered semiconductors where\u0000localized states are significant. Quantitative description of MTR, however, has\u0000been based on an \"abrupt\" mobility edge model, which relies on two underpinning\u0000simplifications: (i) states above the conduction band mobility edge are\u0000extended and any of them is omnipresent in space, whereas states below the\u0000mobility edge are localized and they exist in space as pointlike sites; (ii)\u0000all states are evenly distributed in space, and the local density of states\u0000(DOS) distribution is spatially invariant. The prequel to this paper [Y. Luo\u0000and A. J. Flewitt, Phys. Rev. B 109, 104203 (2024)] demonstrates that neither\u0000of these simplifications is valid. Hence, this paper reinvestigates MTR\u0000transport and focuses on two similar scenarios: steady DC conduction and\u0000non-dispersive time-of-flight conduction. We have managed to reveal that,\u0000first, the experimentally measured mobility edge is an effective quantity which\u0000is different from the actual critical energy that demarcates extended states\u0000and localized states of an amorphous semiconductor. Second, the experimentally\u0000derived extended-state mobility is also an effective quantity which turns out\u0000to be higher than the actual mobility of free electrons in the material. These\u0000two effective quantities are quantified using the hydrogenated amorphous\u0000silicon (a-Si:H) discussed in the prequel paper as an example.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vincent Lahoche, Dine Ousmane Samary, Parham Radpay
This paper examines the quantum $(2+p)$-spin dynamics of a $N$-vector $textbf{x}in mathbb{R}^N$ through the lens of renormalization group (RG) theory. The RG is based on a coarse-graining over the eigenvalues of matrix-like disorder, viewed as an effective kinetic whose eigenvalue distribution undergoes a deterministic law in the large $N$ limit. We focus our investigation on perturbation theory and vertex expansion for effective average action, which proves more amenable than standard nonperturbative approaches due to the distinct non-local temporal and replicative structures that emerge in the effective interactions following disorder integration. Our work entails the formulation of rules to address these non-localities within the framework of perturbation theory, culminating in the derivation of one-loop $beta$-functions. Our explicit calculations focus on the cases $p=3$, $p=infty$, and additional analytic material is given in the appendix.
{"title":"Large time effective kinetics $β$-function for quantum (2+p)-spin glass","authors":"Vincent Lahoche, Dine Ousmane Samary, Parham Radpay","doi":"arxiv-2408.02602","DOIUrl":"https://doi.org/arxiv-2408.02602","url":null,"abstract":"This paper examines the quantum $(2+p)$-spin dynamics of a $N$-vector\u0000$textbf{x}in mathbb{R}^N$ through the lens of renormalization group (RG)\u0000theory. The RG is based on a coarse-graining over the eigenvalues of\u0000matrix-like disorder, viewed as an effective kinetic whose eigenvalue\u0000distribution undergoes a deterministic law in the large $N$ limit. We focus our\u0000investigation on perturbation theory and vertex expansion for effective average\u0000action, which proves more amenable than standard nonperturbative approaches due\u0000to the distinct non-local temporal and replicative structures that emerge in\u0000the effective interactions following disorder integration. Our work entails the\u0000formulation of rules to address these non-localities within the framework of\u0000perturbation theory, culminating in the derivation of one-loop\u0000$beta$-functions. Our explicit calculations focus on the cases $p=3$,\u0000$p=infty$, and additional analytic material is given in the appendix.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marcell D. Kovács, Christopher J. Turner, Lluis Masanes, Arijeet Pal
Floquet quantum circuits are able to realise a wide range of non-equilibrium quantum states, exhibiting quantum chaos, topological order and localisation. In this work, we investigate the stability of operator localisation and emergence of chaos in random Floquet-Clifford circuits subjected to unitary perturbations which drive them away from the Clifford limit. We construct a nearest-neighbour Clifford circuit with a brickwork pattern and study the effect of including disordered non-Clifford gates. The perturbations are uniformly sampled from single-qubit unitaries with probability $p$ on each qubit. We show that the interacting model exhibits strong localisation of operators for $0 le p < 1$ that is characterised by the fragmentation of operator space into disjoint sectors due to the appearance of wall configurations. Such walls give rise to emergent local integrals of motion for the circuit that we construct exactly. We analytically establish the stability of localisation against generic perturbations and calculate the average length of operator spreading tunable by $p$. Although our circuit is not separable across any bi-partition, we further show that the operator localisation leads to an entanglement bottleneck, where initially unentangled states remain weakly entangled across typical fragment boundaries. Finally, we study the spectral form factor (SFF) to characterise the chaotic properties of the operator fragments and spectral fluctuations as a probe of non-ergodicity. In the $p = 1$ model, the emergence of a fragmentation time scale is found before random matrix theory sets in after which the SFF can be approximated by that of the circular unitary ensemble. Our work provides an explicit description of quantum phases in operator dynamics and circuit ergodicity which can be realised on current NISQ devices.
在这项工作中，我们研究了随机 Floquet-Clifford 电路中算子局部化和混沌出现的稳定性，这些电路受到单位扰动，使其偏离克利福德极限。我们构建了一个具有砖砌模式的最近邻克利福德电路，并研究了包含无序非克利福德门的影响。扰动是从单量子比特单元中均匀采样的，每个量子比特上的概率为 $p$。我们证明，在0 le p < 1$的情况下，相互作用模型表现出很强的操作数局部化，其特征是由于墙配置的出现，操作数空间被分割成互不相连的扇区。这些墙导致我们精确构造的电路出现局部运动积分。我们通过分析确定了局部运动对一般扰动的稳定性，并计算出了可由 $p$ 调整的算子扩散平均长度。虽然我们的电路在任何双分区上都是不可分离的，但我们进一步证明，算子局部化会导致纠缠瓶颈，即最初未纠缠的状态在典型片段边界上保持弱纠缠。最后，我们研究了频谱形式因子（SFF），以描述算子片段的混沌特性和作为非极性探测器的频谱波动。在 $p =1$ 模型中，我们发现，在秩矩阵理论形成之前，会出现一个碎片时间尺度，之后，SFF 可以用圆形单元集合的时间尺度来近似。我们的工作明确描述了算子动力学和电路遍历性中的量子相，这可以在当前的 NISQ 器件上实现。
{"title":"Operator space fragmentation in perturbed Floquet-Clifford circuits","authors":"Marcell D. Kovács, Christopher J. Turner, Lluis Masanes, Arijeet Pal","doi":"arxiv-2408.01545","DOIUrl":"https://doi.org/arxiv-2408.01545","url":null,"abstract":"Floquet quantum circuits are able to realise a wide range of non-equilibrium\u0000quantum states, exhibiting quantum chaos, topological order and localisation.\u0000In this work, we investigate the stability of operator localisation and\u0000emergence of chaos in random Floquet-Clifford circuits subjected to unitary\u0000perturbations which drive them away from the Clifford limit. We construct a\u0000nearest-neighbour Clifford circuit with a brickwork pattern and study the\u0000effect of including disordered non-Clifford gates. The perturbations are\u0000uniformly sampled from single-qubit unitaries with probability $p$ on each\u0000qubit. We show that the interacting model exhibits strong localisation of\u0000operators for $0 le p < 1$ that is characterised by the fragmentation of\u0000operator space into disjoint sectors due to the appearance of wall\u0000configurations. Such walls give rise to emergent local integrals of motion for\u0000the circuit that we construct exactly. We analytically establish the stability\u0000of localisation against generic perturbations and calculate the average length\u0000of operator spreading tunable by $p$. Although our circuit is not separable\u0000across any bi-partition, we further show that the operator localisation leads\u0000to an entanglement bottleneck, where initially unentangled states remain weakly\u0000entangled across typical fragment boundaries. Finally, we study the spectral\u0000form factor (SFF) to characterise the chaotic properties of the operator\u0000fragments and spectral fluctuations as a probe of non-ergodicity. In the $p =\u00001$ model, the emergence of a fragmentation time scale is found before random\u0000matrix theory sets in after which the SFF can be approximated by that of the\u0000circular unitary ensemble. Our work provides an explicit description of quantum\u0000phases in operator dynamics and circuit ergodicity which can be realised on\u0000current NISQ devices.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"367 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The thermal conductivity of glasses is well-known to be significantly harder to theoretically describe compared to crystalline materials. Because of this fact, the fundamental understanding of thermal conductivity in glasses remain extremely poor when moving beyond the case of simple glasses, e.g., glassy SiO$_2$, and into so-called 'modified' oxide glasses, that is, glasses where other oxides (e.g. alkali oxides) have been added to break up the network and alter e.g. elastic and thermal properties. This lack of knowledge is apparent despite how modified glasses comprise the far majority of known glasses. In the present work we study an archetypical series of sodium silicate ($xtext{Na}_2text{O}text{-}(100text{-}x)text{SiO}_2$) glasses. Analyses of modal contributions reveal how increasing Na$_2$O content induces increasing vibrational localization with a change of vibrations to be less ordered, and a related general decrease in modal contributions to thermal conductivity. We find the vibrational phases (acoustic vs. optical) of sodium vibrations to be relatively disordered compared to the network-forming silicon and oxygen species, explaining how increasing Na$_2$O content decreases thermal conductivity. Our work sheds new light on the fundamentals of glassy heat transfer as well as the interplay between thermal conduction and modal characteristics in glasses.
{"title":"Thermal conductivity in modified oxide glasses is governed by modal phase changes","authors":"Philip Rasmussen, Søren Strandskov Sørensen","doi":"arxiv-2408.00813","DOIUrl":"https://doi.org/arxiv-2408.00813","url":null,"abstract":"The thermal conductivity of glasses is well-known to be significantly harder\u0000to theoretically describe compared to crystalline materials. Because of this\u0000fact, the fundamental understanding of thermal conductivity in glasses remain\u0000extremely poor when moving beyond the case of simple glasses, e.g., glassy\u0000SiO$_2$, and into so-called 'modified' oxide glasses, that is, glasses where\u0000other oxides (e.g. alkali oxides) have been added to break up the network and\u0000alter e.g. elastic and thermal properties. This lack of knowledge is apparent\u0000despite how modified glasses comprise the far majority of known glasses. In the\u0000present work we study an archetypical series of sodium silicate\u0000($xtext{Na}_2text{O}text{-}(100text{-}x)text{SiO}_2$) glasses. Analyses of\u0000modal contributions reveal how increasing Na$_2$O content induces increasing\u0000vibrational localization with a change of vibrations to be less ordered, and a\u0000related general decrease in modal contributions to thermal conductivity. We\u0000find the vibrational phases (acoustic vs. optical) of sodium vibrations to be\u0000relatively disordered compared to the network-forming silicon and oxygen\u0000species, explaining how increasing Na$_2$O content decreases thermal\u0000conductivity. Our work sheds new light on the fundamentals of glassy heat\u0000transfer as well as the interplay between thermal conduction and modal\u0000characteristics in glasses.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"131 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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